Question

Show that the bisectors of angles of a parallelogram form a rectangle.​

Answer 1

To prove: MNOP is a rectangle.

In parallelogram ABCD

∠A=∠D=90⁰

[they form a straight line]

∴IN△AMD,∠M=90⁰

∠M=∠N=90⁰

[they form a straight line]

Similarly,

∠M=∠P=90⁰

And

∠P=∠O=90⁰

∴∠MPO=∠PON∠ONM=∠NMO=90⁰

∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90⁰]

Answer 2

Answer:

ANSWER

To prove: MNOP is a rectangle.

In parallelogram ABCD

∠A=∠D=90

∘

[they form a straight line]

∴IN△AMD,∠M=90

∘

∠M=∠N=90

∘

[they form a straight line]

Similarly,

∠M=∠P=90

∘

And

∠P=∠O=90

∘

∴∠MPO=∠PON∠ONM=∠NMO=90

∘

∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90

∘

]